You’ve learned all the key elements to programming. Variable, conditionals and loops allow you to do pretty much anything your computer can do. But your code will quickly become hard to read if you simply write everything line after line and copy-and-paste pieces of code you want to re-use.

Functions allow you to a) reuse your code and b) make it easier to read by hiding away the guts in clear, descriptive, and reusable commands.


A Simple Example§

For instance, if we have a pair of points in space, pt1 and pt2, with (X,Y) coordinates. We could find the distance between those using Pythagoras’ theorem:

pt1 = [8.0, 5.3]
pt2 = [2.1, 9.2]
sep1 = ((pt1[0]-pt2[0])**2+(pt1[1]-pt2[1])**2)**0.5

Now, the problem is that a) each time you see that in your code you’ll have to spend a moment working out why it’s there, and b) each time you write it you might make a mistake.


A Simple Example§

Let’s re-use the code for two more variables later in our script:

pt3 = [3.0, 8.1]
pt4 = [2.5, 4.2]
sep2 = ((pt3[0]-pt4[0])**2+(pt1[1]-pt4[1])**2)**0.5

Can you spot the mistake?


A Simple Example§

pt3 = [3.0, 8.1]
pt4 = [2.5, 4.2]
sep2 = ((pt3[0]-pt4[0])**2+(pt1[1]-pt4[1])**2)**0.5

Did you notice that when I changed the pt1,pt2 values to pt3,pt4 I missed one? Hard bugs to spot, right?

A solution is to write functions to do these simple jobs and hide away the hard-to-read pieces of code so that the rest is clear. In this case we want a function that takes two values and finds their separation.


A Simple Example§

Type this function in (if you do this in the shell then press an extra <return> when you’re done to dedent the definition of the function):

def separation(a, b):
    """Get the distance between two points"""
    sep = ((a[0]-b[0])**2+(a[1]-b[1])**2)**0.5
    return sep

Having defined that function you can use it repeatedly:

sep1 = separation(pt1, pt2)
sep2 = separation(pt3, pt4)


Did you notice how help was provided for the function when you started the brackets? It was based on the “””textHere””” in your separation function. In Python these are called docstrings.

Almost any time you’re planning to do something multiple times in a script you should think about replacing it with a function.


Function inputs§

On the whole you should assume that your function only knows about the things that it was given in the first line (you can also have global variables that can be seen from anywhere, but these are generally to be avoided). In the function above we required two variables and these were given the names a and b as we received them (it doesn’t matter what names they had in the script).

Python allows you to specify the inputs to a function by order (“positional” arguments), or name (“named” arguments), or by a combination or order and name. e.g. we could have called the function like this:

sep1 = separation(a, b=pt2)

Function inputs§

You can also provide default values for inputs so that these don’t have to be specified each time. For instance:

def separation(a, b=[0,0]):
    """Get the distance between two points, or from the origin for a single point"""
    sep = ((a[0]-b[0])**2+(a[1]-b[1])**2)**0.5
    return sep

sep3 = separation(pt4) #b is set to [0,0]

Function inputs§

Because we can use names for the arguments, we don’t have to specify all those that precede the one we care about. e.g.:

def separation(a, b=[0,0], verbose=False):
    """Get the distance between two points, or from the origin for a single point"""
    if verbose:
        print('vertical sep=', a[1]-b[1])
        print('horizontal sep=', a[0]-b[0])
    sep = ((a[0]-b[0])**2+(a[1]-b[1])**2)**0.5
    return sep

sep4 = separation(a=pt3, verbose=True) #use first and last args, middle is default
sep5 = separation(pt4, pt2, verbose=True) #can combine ordered args and names
sep6 = separation(a=pt4, pt2) #error? after a named arg, all others must be named

Function outputs§

Some functions don’t need to return anything (they just perform an operation like present a stimulus). The function above returns a single value. You can return multiple values too. Or you can choose whether to return one or more values in the function (this might not be wise though!):

def separation(a, b=[0,0], verbose=False):
    """Get the distance between two points, or from the origin for a single point"""
    vert = a[1]-b[1]
    horiz = a[0]-b[0]
    sep = (vert**2 + horiz**2)**0.5
    if verbose:
        print('vertical sep=', vert)
        print('horizontal sep=', horiz)
        return sep, horiz, vert
        return sep

Function outputs§

sep5, horiz5, vert5 = separation(pt4, pt2, verbose=True)
#or store them as a tuple of 3 values:
sepInfo5 = separation(pt4, pt2, verbose=True)

If you don’t specify any return values in your function but you then try to assign a variable to the output, then that variable will just become equal to the special python value None (i.e. it doesn’t automatically raise an error).


Operations in-place§

Remember that Python passes pointers to objects rather than copies of them, unless you manually make a copy. So again, if you do anything that changes the variable ‘in-place’ then it will be changed in the code that called your function.:

def change(input):
    input[0] = 'a'

myList = [1,2,3]
new = change(myList)
print(new) #surprise? (see note above)
print(myList) #should have changed


You can group functions that you use repeatedly or have a similar purpose together into a single file so that you don’t end up rewriting them over and over again at the top of your script.


Example 1§

Save your separation function into a file called Now, in the same directory, create a new file (e.g. ‘’):

import tools

You could also do:

from tools import separation
print(separation([1,2],[6,4])) #now we don't need tools.______
from tools import * #Not recommended

Example 1§

And you can even rename things as you import them. numpy is a common library for numerical operations (as we’ve seen) and most people import that like this so that it only takes 2 characters to call the functions:

import numpy as np

So that syntax of a dot is used in various ways in Python:

import numpy, os
os.getcwd() #the getcwd function in os module
numpy.random.rand() #the rand function in the random submodule of numpy
("hello").upper() #the upper method of a string object

Example 1§

You can also have multiple modules within a folder. Then you may also need to add a file called which can, optionally, run some code every time you import things from this folder. e.g. I might have a folder in my home directory like:


Example 1§

I can do this in any Python script I run if I add jwpTools to my path (see below):

from jwpTools import sounds, filters
import jwpTools.geometry as geom

Adding a location to your path§